In a force balanced sensing instrument, such as an accelerometer for example, it is generally desired that the instrument output signal be proportional to the input condition to be sensed. Therefore, in many types of electrostatic and electromagnetic force balanced sensing instruments special techniques are required to obtain a linear relation between the instrument output and the sensed input. In electrostatic and electromagnetic instruments, the forces applied by the instrument forcer are not linearly related to the feedback voltage or current supplied to the forcer. Furthermore, for optimum operation of the instrument itself it is preferred that the feedback force applied by the feedback control network have a linear relation to the sensed input. Thus, special techniques have been employed for obtaining such linearity.
As one example, in an electrostatic force balanced accelerometer, electrostatic forcing in a closed loop system is employed to position and obtain an output from a pendulous inertial mass or proof mass. The electrostatic forcing system employs a capacitive pickoff electrode on each side of a pendulous member that has been etched from a silicon substrate. A control pulse is employed to sequentially apply a constant amount of charge to each electrode. A variable force is applied to the inertial mass by varying the amount of time (e.g., duty cycle) the charge is left on a respective plate. The amount of time the charge is left on a respective plate is based on the displacement of the inertial mass relative to a null position.
Accelerometer scale-factor and bias uncertainty can be major sources of error in inertial measurement and/or navigation systems. Bias uncertainty can arise due to transient behavior at turn on, non-modelability, and instability of bias versus temperature characteristics including hysteresis and can simply trend over time. Scale-factor errors can result from a variety of sources, such as effects arising from non-uniform electrical charge distribution, sensing signal asymmetry, material considerations, and environmental conditions. Mitigation of accelerometer scale-factor and bias uncertainty, particularly in a dynamic environment, could significantly improve the performance of inertial measurement and navigation systems.